Lens design

A sharper focus

THEORETICAL physicists have a knack of asking “why not?” Antimatter was discovered because a theoretician called Paul Dirac saw that one of his equations had two solutions: one with a plus sign that predicted normal negatively charged electrons, the other with a minus sign that predicted a curious positively charged beast. Back in 1928, Dirac had the temerity to take the second solution seriously, and today the beast is a tamed antiparticle known as a positron. In similar vein, John Pendry of Imperial College, London has been asking what happens if a material's refractive index, which measures how much it bends a ray of light or other form of electromagnetic radiation, is negative instead of positive—an idea that folk familiar with practical optics might dismiss as absurd. Some of his conclusions are almost as counter-intuitive as positrons. Yet, if they are right, they could prove revolutionary for the design of new types of lenses.

To understand Dr Pendry's line of thought, consider first the common-or-garden variety of refractive index. When a ray of light crosses the boundary between two materials, such as air and glass, its path is deflected. For the geometrically minded, the refractive index is the ratio of the sine of the angle of the incident ray to the sine of the angle of the transmitted ray—both angles measured from a line perpendicular to the boundary. For those who are less geometrically minded, this means that if the light ray is bent away from the boundary, the refractive index is larger than one. This bending, when allied to a curved surface, is responsible for the focusing properties of a glass lens.

The typical value of the refractive index of glass is about 1.4. Bending the other way, towards the boundary, implies a refractive index less than one. This is known to occur for X-rays, but it is uncommon for longer-wave radiation such as light and radio. Dr Pendry's idea, however, is more radical still: a refractive index that is not merely less than one, but less than zero. Geometrically at least, it makes perfect sense. In a material with an index of, say, -1, the angle of deflection of the light ray would be equal to the angle of incidence, but in the opposite direction. So a flat slab of such a material would send all the rays originating from a single point back to a mirror-image point on the other side of the slab. It would act as a lens without requiring any of the specially curved surfaces that normal lenses demand.

This much had already been deduced nearly 40 years ago. But Dr Pendry's bold conclusion, just published in Physical Review Letters, is that a slab of material with a negative refractive index would not merely make a nice lens, it would make a perfect lens. This is because such a lens need not be limited by an imperfection known as the diffraction limit, which has set a ceiling on the accuracy of optical systems ever since lenses were first polished.

That is an altogether more subtle claim. The diffraction limit occurs because normal lenses, no matter how carefully formed, do not pick up all the electromagnetic waves emitted by an object. Some of these waves of electrical and magnetic energy travel over long distances, and are known in the jargon as the far field. But other components, known as the near field, die out quickly as they leave their source. Because the near field usually never gets to the image, information is lacking about the source. This missing information is what limits the resolution of a lens to roughly half the wavelength of the radiation used.

Dr Pendry's calculations for a material with a negative refractive index, rather like Dirac's for the electron, have two solutions—and the second allows near-field waves to grow instead of decaying. In the right circumstances this effect can exactly balance out the decay, ensuring that all the information is restored in a perfect image of the source. The wavelength of visible light is a fraction of a millionth of a metre, which sets a resolution limit for conventional optical microscopes. But with negative-refractive-index lenses, this limit could be removed.

That is all very well on paper, but there are no known materials with optical properties of anything like a refractive index of -1. Fortunately, the electromagnetic spectrum is broader than the visible section that eyes detect. Earlier this year, Sheldon Schultz at the University of California, San Diego, showed that a specially designed material made of wires and rings had a negative refractive index in the microwave region. Meanwhile Dr Pendry and his colleagues at Hammersmith Hospital in London, along with GEC Marconi, an electronics company, have designed a negative-refractive-index lens for radio waves on the same principles.

One practical application of these radio lenses could be to focus the radio waves used in magnetic-resonance imaging (MRI), a form of medical body-scanning. Instead of bathing a patient with radio waves, it might become possible to focus the radio energy on the organ of interest, even though bodily organs are smaller than the radio wavelength used in MRI, which is typically a metre. The technique remains unproven, but early efforts by Dr Pendry and his colleagues seem promising. And Dr Pendry already has ideas about how to build lenses that would do the same job in the optical region. For generations of scientists, the diffraction limit was seen as a fundamental barrier to progress in optics, so news of perfect lenses will come as a shock to some. But then, so did antimatter.